Secure Performance Analysis for Multi-Pair AF Relaying Massive MIMO Systems in Ricean Channels

This paper investigates the secure communication in a multi-pair massive multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay network over Ricean fading channels in the presence of an eavesdropper. With the imperfect estimated channel state information, maximum ratio combining (MRC)/maximal ratio transmission (MRT) are employed for AF relaying. Based on random matrix theory, we first derive tractable analytical expressions of the end-to-end signal-to-interference-plus-noise ratios (SINRs) at the intended user and Eve, respectively. Then, some asymptotic results for infinite Ricean K-factor, unbounded transmit power, and relay power are provided, which show that the SINRs at target user and Eve are both limited by some bounds and the effects of estimation error, relay noise, or received additive noise will be eliminated in these extreme cases. Meanwhile, power scaling laws for transmit power and relay power are studied that they should satisfy to maintain a desirable rate level. Analytical results indicate that the power can largely be cut down in inverse proportion to the number of relay antennas in Ricean fading channels. Moreover, by exploiting successive approximations, geometric programming, and iterative computation, a power control scheme is proposed to maximize the achievable sum secrecy rate. Numerical results are presented to demonstrate the effectiveness of this secure multi-pair massive MIMO relaying system.